Object distance and magnifiation

[996gt2]

1. The problem statement, all variables and given/known data

A 6mm diameter microscope objective has focal length 9mm.

What object distance is required to achieve a lateral magnification of -40?

2. Relevant equations

mobj=-L/fobj


3. The attempt at a solution

-40x=-L/9mm

L=360mm

Why isn't the answer 360mm? I think it might have something to do with the diameter of the lens, but I'm not completely sure. Can someone explain? Thanks!

[996gt2]

Anyone?

[Redbelly98]

Check out two of the equations here:
http://www.physicsforums.com/library.php?do=view_item&itemid=148

You need the Gaussian lens formula, as well as the expression for magnification m given there.

[996gt2]

Well, the formula I included is basically an approximation derived from the Gaussian lens formula...at least, that's how my book put it.

Basically, with a microscope, the object is very very close to the focal point, so s\approxf. Similarly, the focal length of the objective is much less than the length of the microscope tube, so s'\approxL

Is it wrong to use these adapted formulas from the book?

[Redbelly98]

Yes, the object distance will be close to f=9mm. So your answer of 360mm is way way off.

[996gt2]

Hmmm, after some thinking I got:

1/f=1/s+1/s'
1/9mm=1/x+1/40x
x=9.225mm


And it was right! Thanks for the suggestion to use the Gaussian optics formulas :)